Linear system state estimation problem: From the received signal \(\mathbf {y}\)  collected across RRHs, we are interested in finding an estimate \(\mathbf {\hat{s}}\)  of the state vector \(\mathbf {s}\) . In this paper, we focus on the centralized C-RAN architecture, where all the BBUs are collocated at the central C-RAN node. Thus, due to availability of \(\mathbf {y}\)  at the central location, we consider centralized algorithms for the state estimation problem. However, the solution we propose in this paper is based on GBP framework, thus it is easily adaptable to a distributed scenario that we refer to as fog-RAN (F-RAN), where BBUs are distributed across different geographic locations closer to the MTC UEs. We refer the interested reader to our recent overview of distributed algorithms for solving the state estimation problem in the context of upcoming 5G cellular networks [1]}.
